Analytic General Solution of the Riccati equation
Exactly Solvable and Integrable Systems
2026-04-09 v4
Abstract
A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytic general solution is presented, which can be extended to second-order linear ordinary differential equation. This result may provide valuable mathematical criteria for in-depth research on quantum mechanics, relativity and dynamical systems.
Cite
@article{arxiv.2510.19297,
title = {Analytic General Solution of the Riccati equation},
author = {Zhao Ji-Xiang},
journal= {arXiv preprint arXiv:2510.19297},
year = {2026}
}
Comments
Fixed some bugs from the previous version